If they are in regular soft nursery pots, cut the bottoms off the pots (when you can plant them outdoors) and dig holes where you want them to grow. Set the bottomless pot in the hole, cover it up and let it grow - no need to remove the whole pot - just cut the bottoms out of the pot they are growing in - set the whole bottomless pot, with vines growing, down in the hole - it should be safe to set them out very soon in your area.

As for supports, you can make something out of regular tree branches for them to climb on.

Thanks, kayjones, but I'm worried about support for the time between now and planting. These shoots are getting taller by the second, it seems, and I don't want them all fallen-over and tangled up while they're still in their peat pots in my basement under the grow lights! But I still need to be able to train them onto their permanent support when I plant them outdoors.

Sweet peas have deep roots so I always start mine in toilet roll inners. You can get special deep pots for them. I start mine in January in my glass porch and have just planted them out this past weekend but it's about 52f here.

I know it is hard to do but you will get more blooms if you pinch them out several times. Nip off the shoots just above a pair of leaves. You want multiple stems not just a single one, unless you are growing for show purposes. You also don't want 'tall slender green shoots' - you want short sturdy multiple green shoots. Grow them as cool and as light as possible to slow them down and keep them strong. I would put them outdoors whenever it is not actually freezing. Grow them 'hard'. They should not need supports until you plant them out. If they do they have been grown too soft. Good luck.

Thank you flora! I thought about pinching them back; some of them have a couple of sets of leaves. And I have considered putting them out, even when it's hovering around freezing, as long as they're in sun.

I shall nip them tonight.